Today is an era of wireless communication systems. The day is not so far when the whole distributed system of the world will goes wireless. Leader in a distributed system plays a vital role in various computing environments like wireless networks etc. The main focus of researchers is on electing a new leader with lesser time consumption and with transmitting minimum number of messages in the network. Election of a leader using binary heap tree mechanism has garnered attention recently. But there are many other variants of heaps available in the literature which has better running time as compared to binary heaps. This paper presents design of leader election algorithm using a better variant called Fibonacci heap structure.